I've run in to the question of parameterising a complex trig function, say sin(z), in the form (x(t),y(t)) for t over some reasonable interval, say [0,2pi].
The question specifically, and in fact only, asks for the parameterisation of the function, in that form, over that interval.
I'm tempted to say this is a simple case of
z(t)= (t,sin(t)) but I feel I'm missing something more fundamental to complex numbers.
I've got sin(z) in terms of its real and imaginary parts, eg
sin(z)=sin(x)cosh(y)+icos(x)sinh(y)
this seems like the way to go, but how would I go about putting t in there?